The development of frequency-scanning interferometers that use multiple laser frequencies, or wavelengths, to perform measurements has been underway for several years. The interferometers are especially useful for measuring surface profiles of test objects as measures of surface variations taken normal to a reference plane or surface. References exemplifying this development include:                R. G. Pilston and G. N. Steinberg, “Multiple-Wavelength Interferometry with Tunable Source,” Applied Optics 8 (1969) 553–556.        D. Malacara, editor, “Optical Shop Testing”, New York, Wiley (1978) 397–402.        Y. Cheng and J. C. Wyant, “Multiple-Wavelength Phase-Shifting Interferometry,” Applied Optics 24 (1985) 804.        
More recent developments of frequency-scanning interferometry include the use of components such as tunable diode lasers and CCD detector arrays. As a result, compact, accurate, and fast systems have been developed, which have the capability of performing quality control measurements on many varieties of commercial precision parts. Examples of these more recent developments include:                H. Kikuta, K. Iwata, and R. Nagata, “Distance Measurement by Wavelength Shift of Laser Diode Light,” Applied Optics 25 (1986) 2976–2980.        T. Kubota, M. Nara, and T. Yoshino, “Interferometer for Measuring Displacement and Distance,” Optics Letters 12 (1987) 310–312.        P. de Groot, “Three-Color Laser-Diode Interferometer,” Applied Optics 30 (1991) 3612–3616.        M. Suematsu and M. Takeda, “Wavelength-Shift Interferometry for Distance Measurement using a Fourier Transform Technique for Fringe Analysis,” Applied Optics 30 (1991) 4046–4055.        J. C. Marron and K. S. Schroeder, “Three-Dimensional Lensless Imaging Using Laser Frequency Diversity,” Applied Optics 31 (1992) 255–262.        J. C. Marron and K. S. Schroeder, “Holographic Laser Radar,” Optics Letters 18 (1993) 385–387.        R. G. Paxman, J. H. Seldin, J. R. Fienup, and J. C. Marron, “Use of an Opacity Constraint in Three-Dimensional Imaging,” In Proceedings of the SPIE Conference on Inverse Optics III, 2241, Orlando, Fla., April 1994.        L. G. Shirley and G. R. Hallerman, “Applications of Tunable Lasers to Laser Radar and 3D Imaging,” Technical Report 1025, Lincoln Laboratory, MIT, Lexington, Mass., 1996.        S. Kuwamura and I. Yamaguchi, “Wavelength Scanning Profilometry for Real-Time Surface Shape Measurement,” Applied Optics 36 (1997) 4473–4482.        J. C. Marron and Kurt W. Gleichman, “Three-Dimensional Imaging Using a Tunable Laser Source,” Optical Engineering 39 (2000) 47–51.        
All of these references from both lists are hereby incorporated by reference for purposes including identifying conventional apparatus and processing algorithms used in the practice of frequency-scanning interferometry.
A known type of frequency-scanning interferometer system 10 is depicted in prior art FIG. 1. While in the overall form of a Twyman-Green interferometer, a tunable laser 12 under the control of a computer 14 produces a measuring beam 16 that can be tuned through a range of different frequencies. Beam-conditioning optics 18 expand and collimate the measuring beam 16. A folding mirror 20 directs the measuring beam 16 to a beamsplitter 22 that divides the measuring beam 16 into an object beam 24 and a reference beam 26. The object beam 24 retroreflects from a test object 30, and the reference beam 26 retroreflects from a reference mirror 32. The beamsplitter 22 recombines the object beam 24 and the reference beam 26, and imaging optics 34 (such as a lens or group of lenses) focus overlapping images of the test object 30 and the reference mirror 32 onto a detector array 36 (such as a CCD array of elements). The detector array 36 records the intensity of an interference pattern produced by path length variations between the object and reference beams 24 and 26. Outputs from the detector array 36 are stored and processed in the computer 14.
The elements of the detector array 36 record local intensity values subject to the interference between the object and reference beams 24 and 26. Each of the intensity values is traceable to a spot on the test object 30. However, instead of evaluating intensity values to determine phase differences between the object and reference beams 24 and 26 as a primary measure of surface variation, a set of additional interference patterns is recorded for a series of different illumination frequencies (or wavelengths) of the measuring beam 16. The tunable laser 12 is stepped through a succession of incrementally varying illumination frequencies, and the detector array 36 records the corresponding interference patterns. Data frames recording individual interference patterns numbering 16 or 32 frames are typical.
The local intensity values vary sinusoidally with changes in illumination frequency between conditions of constructive and destructive interference. The rate of intensity variation, i.e., the frequency of intensity variation, is a function of the path length difference between the local portions of the object and reference beams 24 and 26. Gradual changes in intensity (lower interference frequency variation) occur at small path length differences, and more rapid changes in intensity (higher interference frequency variation) occur at large path length differences.
Discrete Fourier transforms can be used within the computer 14 to identify the interference frequencies of intensity variation accompanying the incremental changes in the illumination frequency of the measuring beam 16. The computer 14 also converts the interference frequencies of intensity variation into measures of local path length differences between the object and reference beams 24 and 26, which can be used to construct a three-dimensional image of the test object 30 as measures of profile variations from a surface of the reference mirror 32. Since the reference mirror 32 is planar, the determined optical path differences are equivalent to deviations of the object 30 from a plane. The resulting three-dimensional topographical information can be further processed to measure important characteristics of the object 30 (e.g. flatness or parallelism), which are useful for quality control of precision-manufactured parts.
The intensity values “I” recorded by elements of the detector array 36 can be written as the sum of two coherent components; one from the object beam 24 “Uobj” and one from the reference beam 26 “Uref” as follows:I=|(Uobj+Uref)|2.  (1)
The recorded intensity corresponds, for example, to the intensity measured by a pixel within the image produced by the object and reference beams 24 and 26. The object beam 24 “Uobj” can be written as:
                                          U            obj                    =                                    A              1                        ⁢                          ⅇ                              ⅈ                ⁡                                  (                                                                                    2                        ⁢                                                                                                  ⁢                        π                                            λ                                        ⁢                                          R                      1                                                        )                                                                    ,                            (        2        )            and the reference beam 26 “Uref” as:
                                          U            ref                    =                                    A              2                        ⁢                          ⅇ                              ⅈ                ⁡                                  (                                                                                    2                        ⁢                                                                                                  ⁢                        π                                            λ                                        ⁢                                          R                      2                                                        )                                                                    ,                            (        3        )            where “A1” and “A2” are the amplitudes, “λ” is the wavelength, and “R1” and “R2” are the optical paths for the two beams 24 and 26. Considering the path difference as R=R1−R2, intensity “I” can be written as:
                              I          =                      |                          A              1                        ⁢                          |              2                        ⁢                          +                              |                                  A                  2                                ⁢                                  |                  2                                ⁢                                                      +                    2                                    ⁢                                      A                    1                                    ⁢                                      A                    2                                    ⁢                                      cos                    ⁡                                          (                                                                                                    2                            ⁢                                                                                                                  ⁢                            π                                                    λ                                                ⁢                        R                                            )                                                                                                          ,                            (        4        )            or, using frequency notation:
                              I          =                      |                          A              1                        ⁢                          |              2                        ⁢                          +                              |                                  A                  2                                ⁢                                  |                  2                                ⁢                                                      +                    2                                    ⁢                                      A                    1                                    ⁢                                      A                    2                                    ⁢                                      cos                    ⁡                                          (                                                                                                    2                            ⁢                                                                                                                  ⁢                            π                                                    λ                                                ⁢                        R                        ⁢                                                                                                  ⁢                        V                                            )                                                                                                          ,                            (        5        )            where “c” is the speed of light and “v” is the illumination frequency.
Equation (5) shows that the intensity has two basic terms: a bias term equal to “|A1|2+|A2|2” and a cosine term. The sinusoidal intensity variation of interest arises from the cosine term. The bias term is an offset that can be easily removed by computing the mean of the intensity data and subtracting this mean from Equation (5).
As is also apparent from equation (5), the frequency of the cosine term depends upon the frequency (or wavelength) of the measuring beam 16 and “R”—the optical path difference (OPD). Based on the incremental changes in illumination frequency provided by the tunable laser 12, a value of “R” can be fit to the function using Fourier transform methods. The procedure involves recording the interference patterns for a series of “N” illumination frequencies. The data from each detector element is then Fourier transformed using known (or estimated) illumination frequencies, and the locations of the peak interference frequencies of variation reveal the values of “R” for each detector element.
FIG. 2 shows a typical result of the discrete Fourier transformation of intensity data corresponding to a typical data set of 32 (N) illumination frequencies recorded by a single detector element and fitted to Equation (5) with the mean value of the illumination intensity subtracted. Plotted are the relative amplitudes IK′|2 of the interference frequency divisions sampled within a bandwidth subdivided into 256 (M) equal subdivisions as follows:|K′|2=|FFT(I−Ī)|2,  (6)where I=10 +cos (3πn/10).
Two interference frequency peaks 40 and 42 result from the cosine function, corresponding to opposite signs of path length difference between the object and reference beams 24 and 26. As path length differences “R” increase, one of the peaks 40 or 42 devolves into the other 42 or 40; the exchange determining the range at which the data can be unambiguously converted into profile variations. The determination of which of the peaks 40 or 42 corresponds to the actual path length difference between the object and reference beams 24 and 26 can be made by phase shifting in which the optical path length difference between the object and reference beams 24 and 26 is deliberately altered in a systematic manner. Examples of phase-shifting methods to resolve the “two-peak” ambiguity and extend the measurement interval are disclosed in the previously referenced paper to J. C. Marron and Kurt W. Gleichman, as well as in U.S. Pat. Nos. 4,832,489; 5,777,742; 5,880,841; 5,907,404; and 5,926,277, which are also hereby incorporated herein.
Although phase shifting is routinely used for resolving interference ambiguities, the practice requires additional measurements, complicates measuring apparatus, and consumes processing time. Common-path interferometric systems, such as Fizeau interferometers, are not easily adaptable to phase shifting. Within common-path interferometric systems, the test object can be mounted together with the reference element within a cavity or the test optic can be mounted on the reference element. Additional requirements for systematically changing to the spacing between the test object and the reference element as required for phase shifting add considerable mechanical complexity and weaken the connection between the test object and reference element exploited by common-path interferometry.